1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
zheka24 [161]
2 years ago
15

Please show work and thank youuu

Mathematics
1 answer:
Assoli18 [71]2 years ago
3 0

Answer:  6\sqrt{3}

======================================================

Explanation:

Method 1

We can use the pythagorean theorem to find x.

a^2+b^2 = c^2\\\\6^2+x^2 = 12^2\\\\36+x^2 = 144\\\\x^2 = 144-36\\\\x^2 = 108\\\\x = \sqrt{108}\\\\x = \sqrt{36*3}\\\\x = \sqrt{36}*\sqrt{3}\\\\x = 6\sqrt{3}\\\\

-----------------------------------

Method 2

Use the sine ratio to find x. You'll need a reference sheet or the unit circle, or simply memorize that sin(60) = sqrt(3)/2

\sin(\text{angle}) = \frac{\text{opposite}}{\text{hypotenuse}}\\\\\sin(60^{\circ}) = \frac{x}{12}\\\\\frac{\sqrt{3}}{2} = \frac{x}{12}\\\\x = 12*\frac{\sqrt{3}}{2}\\\\x = 6\sqrt{3}\\\\

-----------------------------------

Method 3

Similar to the previous method, but we'll use tangent this time.

Use a reference sheet, unit circle, or memorize that tan(60) = sqrt(3)

\tan(\text{angle}) = \frac{\text{opposite}}{\text{adjacent}}\\\\\tan(60^{\circ}) = \frac{x}{6}\\\\\sqrt{3} = \frac{x}{6}\\\\x = 6\sqrt{3}\\\\

-----------------------------------

Method 4

This is a 30-60-90 triangle. In other words, the angles are 30 degrees, 60 degrees, and 90 degrees.

Because of this special type of triangle, we know that the long leg is exactly sqrt(3) times that of the short leg.

\text{long leg} = (\text{short leg})*\sqrt{3}\\\\x = 6\sqrt{3}\\\\

The short leg is always opposite the smallest angle (30 degrees).

You might be interested in
Help asap
LenKa [72]
Hello! The answer is 13.5 seconds! I hope this helps :3
5 0
3 years ago
What does this mean: draw an example of a dot plot with 6 data points that has a large variability
NNADVOKAT [17]
Basically make a plot that has no correlation (the points are all random and don't mean anything)

5 0
3 years ago
regular octagon rotates 360° about its center. How many times does the image of the octagon coincide with the preimage during th
Galina-37 [17]
An octagon has 8 sides, a rotation of 45° (360°/8) will map the octagon onto its preimage. Answer is 8.
7 0
3 years ago
A study was conducted to determine whether an expectant mother's cigarette smoking has any effect on the bone mineral content of
svp [43]

Using Hypothesis testing,

a) Two samples are independent.

b)H₀: an expectant mother's cigarette smoking has any not effect on the bone mineral content of her otherwise healthy child.

Hₐ : an expectant mother's cigarette smoking has any effect on the bone mineral content of her otherwise healthy child.

c) Null hypothesis is accepted.

so, an expectant mother's cigarette smoking has no effect on the bone mineral.

We have given that,

A study which is conducted for check an expectant mother's cigarette smoking has any effect on the bone mineral content of her otherwise healthy child.

For new-born whose mother's cigarette smoking

sample size , n₁= 77

X-bar, x₁-bar = 0.098 g/cm

standard deviations, s₁ = 0.026 g/cm

For new-born whose mother did not cigarette smoking

sample size , n₂ = 161

standard deviations, s₂ = 0.025 g/cm.

mean (X-bar) , x₂-bar = 0.095 g/cm

a) the two samples are independent since they are different types of mothers, smoking mothers and non smoking mothers

b)H₀: an expectant mother's cigarette smoking has any not effect on the bone mineral content of her otherwise healthy child.

Hₐ: an expectant mother's cigarette smoking has any effect on the bone mineral content of her otherwise healthy child.

c) Test statistic:

t = (x₁-bar - x₂-bar )/S (√1/n₁+1/n₂)

where , S = √(s₁²(n₁ - 1) + s₂²(n₂ -1))/n₁+n₂ - 2

S = √((0.026)²(76) +(0.025 )²(160))/236

= 0.0253

then, t = (0.098 - 0.095 )/0.0253(√1/77 +1/161 )

=> t = 0.859

Using the critacal table critical t is

Critical t = ±1.970065

Degrees of freedom =236.0000

P-Value=0.3935 which is greater than α(0.05),

So , we accept H₀

Thus, an expectant mother's cigarette smoking has not effect on the bone mineral content of her otherwise healthy child.

To learn more about Hypothesis testing, refer:

brainly.com/question/4232174

#SPJ4

8 0
1 year ago
1 point An old Honda Civic can go 351 miles on average before it runs out of gas. Its tank holds 11 gallons of gas. What is the
ad-work [718]

Answer:

32 miles per gallon

Step-by-step explanation:

351 divided by 11 = 31.90909090909090909090909090 e.t.c

8 0
3 years ago
Other questions:
  • What is the area of rhombus ABCD ?
    13·2 answers
  • What is the scientific notation for the number of kilometers light will travel in 60 seconds
    14·1 answer
  • There is a piece of tape attached to a hula hoop. The tape rotates to (_7, 20) during one spin. What is the sine value of this f
    11·1 answer
  • 3/8 of the seventh grade students were taking advanced math at the beginning of the year, but seven dropped out by the end of th
    5·1 answer
  • What are the weekly wages for 40 hours of work at an hourly rate of $8.50
    5·2 answers
  • Which statement best describes the constant in this expression?
    9·1 answer
  • What is the distance between the points (7,3) and (-8, O) on a coordinate grid?​
    15·1 answer
  • This is not a graded question
    6·1 answer
  • Solve the equation P=k x t / V for the letter k
    14·1 answer
  • What is ( m = 3 and contains (4, -1) in slope intercept form​
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!